{"abstract":"Output bit polarity is inverted for the stipulated density link.","category":"PCM sample encoding","checks":8,"contract":"Convert bounded nonnegative PCM levels no greater than denominator into a deterministic one-bit pulse-density stream, preserving fractional accumulator state.","contract_signature":"samples, denominator, accumulator","evaluation_group":"s3-pcm-pcm-onebit-pulse-density","failed_approach":"Returning amplitude quanta violates the one-bit output representation.","family":"s3-pcm-pcm-onebit-pulse-density-bit-polarity","id":"FA-49706","implementations":{"attempt":{"sha256":"f83a8800d6b5fa4cbc27b202be6ec81975073b768324290b57e661eb7f0117f4","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(samples, denominator, accumulator):\n    bits=[]\n    for sample in samples:\n        accumulator+=sample\n        pulse=accumulator>=denominator\n        if pulse:\n            accumulator-=denominator\n        bits.append(int(pulse)*denominator)\n    return [bits,accumulator]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('oracle 1', solve(*([1, 2, 3, 4], 5, 0)), [[0, 0, 1, 1], 0])\ncheck('oracle 2', solve(*([5, 0, 5], 5, 0)), [[1, 0, 1], 0])\ncheck('oracle 3', solve(*([2, 2, 2, 2], 3, 1)), [[1, 0, 1, 1], 0])\ncheck('oracle 4', solve(*([], 5, 2)), [[], 2])\ncheck('oracle 5', solve(*([0, 0], 4, 3)), [[0, 0], 3])\ncheck('oracle 6', solve(*([3, 3, 3], 4, 2)), [[1, 1, 0], 3])\ncheck('oracle 7', solve(*([1, 1, 1], 2, 0)), [[0, 1, 0], 1])\nif N == 1: check('variant packet 1', solve(*[[1, 2, 3, 4, 1, 2, 3, 4], 5, 0]), [[0, 0, 1, 1, 0, 0, 1, 1], 0])\nif N == 2: check('variant packet 2', solve(*[[1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4], 5, 0]), [[0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1], 0])\nif N == 3: check('variant packet 3', solve(*[[1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4], 5, 0]), [[0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1], 0])\nif N == 4: check('variant packet 4', solve(*[[1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4], 5, 0]), [[0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1], 0])\nif N == 5: check('variant packet 5', solve(*[[1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4], 5, 0]), [[0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1], 0])\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"},"broken":{"sha256":"858b1c7f4690d840a8f128155781f3380caa4b04fe203e16dd21d51c2356cdd7","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(samples, denominator, accumulator):\n    bits=[]\n    for sample in samples:\n        accumulator+=sample\n        pulse=accumulator>=denominator\n        if pulse:\n            accumulator-=denominator\n        bits.append(int(not pulse))\n    return [bits,accumulator]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('oracle 1', solve(*([1, 2, 3, 4], 5, 0)), [[0, 0, 1, 1], 0])\ncheck('oracle 2', solve(*([5, 0, 5], 5, 0)), [[1, 0, 1], 0])\ncheck('oracle 3', solve(*([2, 2, 2, 2], 3, 1)), [[1, 0, 1, 1], 0])\ncheck('oracle 4', solve(*([], 5, 2)), [[], 2])\ncheck('oracle 5', solve(*([0, 0], 4, 3)), [[0, 0], 3])\ncheck('oracle 6', solve(*([3, 3, 3], 4, 2)), [[1, 1, 0], 3])\ncheck('oracle 7', solve(*([1, 1, 1], 2, 0)), [[0, 1, 0], 1])\nif N == 1: check('variant packet 1', solve(*[[1, 2, 3, 4, 1, 2, 3, 4], 5, 0]), [[0, 0, 1, 1, 0, 0, 1, 1], 0])\nif N == 2: check('variant packet 2', solve(*[[1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4], 5, 0]), [[0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1], 0])\nif N == 3: check('variant packet 3', solve(*[[1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4], 5, 0]), [[0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1], 0])\nif N == 4: check('variant packet 4', solve(*[[1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4], 5, 0]), [[0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1], 0])\nif N == 5: check('variant packet 5', solve(*[[1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4], 5, 0]), [[0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1], 0])\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"}},"limitations":"Stipulated finite model; no claim of hardware timing or full file-format conformance. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.","method":"Deterministic executable model with adversarial boundary fixtures.","provenance":{"created_by":"Failure Map","dependencies":"Python standard library","family":"s3-pcm-pcm-onebit-pulse-density-bit-polarity","generated_at":"2026-09-29T14:45:02.435115+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Offline PCM interchange uses these exact bounded packet and sample representation decisions.","root_cause":"Output bit polarity is inverted for the stipulated density link.","sha256":"f458163e52f67a31af23771f941001c4b94bbfaceedc444b4c59460464897cd0","title":"Pcm onebit pulse density: bit polarity · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verified":true,"visibility":"public","verification":{"attempt":{"elapsed_ms":41.004,"exit_code":1,"observations":[{"actual":[[0,0,5,5],0],"check":"oracle 1","expected":[[0,0,1,1],0],"passed":false},{"actual":[[5,0,5],0],"check":"oracle 2","expected":[[1,0,1],0],"passed":false},{"actual":[[3,0,3,3],0],"check":"oracle 3","expected":[[1,0,1,1],0],"passed":false},{"actual":[[],2],"check":"oracle 4","expected":[[],2],"passed":true},{"actual":[[0,0],3],"check":"oracle 5","expected":[[0,0],3],"passed":true},{"actual":[[4,4,0],3],"check":"oracle 6","expected":[[1,1,0],3],"passed":false},{"actual":[[0,2,0],1],"check":"oracle 7","expected":[[0,1,0],1],"passed":false},{"actual":[[0,0,5,5,0,0,5,5],0],"check":"variant packet 1","expected":[[0,0,1,1,0,0,1,1],0],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 1\", \"actual\": [[0, 0, 5, 5], 0], \"expected\": [[0, 0, 1, 1], 0], \"passed\": false}, {\"check\": \"oracle 2\", \"actual\": [[5, 0, 5], 0], \"expected\": [[1, 0, 1], 0], \"passed\": false}, {\"check\": \"oracle 3\", \"actual\": [[3, 0, 3, 3], 0], \"expected\": [[1, 0, 1, 1], 0], \"passed\": false}, {\"check\": \"oracle 4\", \"actual\": [[], 2], \"expected\": [[], 2], \"passed\": true}, {\"check\": \"oracle 5\", \"actual\": [[0, 0], 3], \"expected\": [[0, 0], 3], \"passed\": true}, {\"check\": \"oracle 6\", \"actual\": [[4, 4, 0], 3], \"expected\": [[1, 1, 0], 3], \"passed\": false}, {\"check\": \"oracle 7\", \"actual\": [[0, 2, 0], 1], \"expected\": [[0, 1, 0], 1], \"passed\": false}, {\"check\": \"variant packet 1\", \"actual\": [[0, 0, 5, 5, 0, 0, 5, 5], 0], \"expected\": [[0, 0, 1, 1, 0, 0, 1, 1], 0], \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":40.63,"exit_code":1,"observations":[{"actual":[[1,1,0,0],0],"check":"oracle 1","expected":[[0,0,1,1],0],"passed":false},{"actual":[[0,1,0],0],"check":"oracle 2","expected":[[1,0,1],0],"passed":false},{"actual":[[0,1,0,0],0],"check":"oracle 3","expected":[[1,0,1,1],0],"passed":false},{"actual":[[],2],"check":"oracle 4","expected":[[],2],"passed":true},{"actual":[[1,1],3],"check":"oracle 5","expected":[[0,0],3],"passed":false},{"actual":[[0,0,1],3],"check":"oracle 6","expected":[[1,1,0],3],"passed":false},{"actual":[[1,0,1],1],"check":"oracle 7","expected":[[0,1,0],1],"passed":false},{"actual":[[1,1,0,0,1,1,0,0],0],"check":"variant packet 1","expected":[[0,0,1,1,0,0,1,1],0],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 1\", \"actual\": [[1, 1, 0, 0], 0], \"expected\": [[0, 0, 1, 1], 0], \"passed\": false}, {\"check\": \"oracle 2\", \"actual\": [[0, 1, 0], 0], \"expected\": [[1, 0, 1], 0], \"passed\": false}, {\"check\": \"oracle 3\", \"actual\": [[0, 1, 0, 0], 0], \"expected\": [[1, 0, 1, 1], 0], \"passed\": false}, {\"check\": \"oracle 4\", \"actual\": [[], 2], \"expected\": [[], 2], \"passed\": true}, {\"check\": \"oracle 5\", \"actual\": [[1, 1], 3], \"expected\": [[0, 0], 3], \"passed\": false}, {\"check\": \"oracle 6\", \"actual\": [[0, 0, 1], 3], \"expected\": [[1, 1, 0], 3], \"passed\": false}, {\"check\": \"oracle 7\", \"actual\": [[1, 0, 1], 1], \"expected\": [[0, 1, 0], 1], \"passed\": false}, {\"check\": \"variant packet 1\", \"actual\": [[1, 1, 0, 0, 1, 1, 0, 0], 0], \"expected\": [[0, 0, 1, 1, 0, 0, 1, 1], 0], \"passed\": false}], \"passed\": false}\n"}},"member_only":{"stages":["fixed"],"fields":["implementations.fixed","verification.fixed","harness","repair"],"note":"The verified repair, its recorded checks, the repair description, and the scoring harness are available to members."}}